The most important accuracy-limiting factor for modern space-based geodetic techniques such as Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), the Global Positioning System (GPS), and satellite altimetry is the modeling of atmospheric refraction corrections. SLR uses lasers to measure very precise ranges from ground tracking stations to orbiting geodetic satellites with current single-shot accuracies at the sub-centimeter level.; The current modeling of atmospheric refraction in the analysis of SLR data involves determining the atmospheric delay in the zenith direction and subsequent projection to a given elevation angle, using a mapping function. Improved refraction modeling; is essential in reducing errors in SLR measurements in order to study variations in the Earth's gravity field and crustal motion, as well as monitoring sea-level rise, post-; glacial rebound and other geophysical phenomena. In most of these applications, and particularly for the establishment and monitoring of the International Terrestrial Ref-; erence Frame (ITRF), of great interest is the stability of its scale and its implied height system.; The assumptions of a spherically symmetric atmosphere makes the delay models only dependent on elevation with no dependence on azimuth, and also results in their total failure to account for horizontal refractivity gradient effects. The work in this; dissertation has been based on developing an accurate two-dimensional (2D) and three-dimensional (3D) ray tracing technique, specifically tailored to use globally distributed data from the Atmospheric Infrared Sounder (AIRS), the European Center for Medium Weather Forecasting (ECMWF) and the National Center for Environmental Prediction (NCEP) in order to compute the atmospheric delay, including contributions from horizontal refractivity gradients. We demonstrate the accuracy and effectiveness of the; ray tracing technique by applying the results to a two-year set of global SLR geodetic data with 47,664 observations from the LAGEOS 1 and 2 geodetic satellites. Replacing the delay model with 3D ray tracing significantly reduced the variance of the SLR; solution residuals, a very important result with regard to future improvements of the the accuracy and stability of the ITRF.